I suspected the process could be expressed and evaluated in mathematical terms, as your linked article explained in their example (BTW the linked site now omits the referenced pictures). But my "monkey brain" cannot intuit how ANY maneuvering of the string (e.g. looping it over the post) can circumvent the inescapable necessity of disconnecting the string from the post to free the ring. Maybe my monkey brain can grasp what's happening better if I build a model and watch the process carefully, then even try to do the reverse operation of putting the ring back on the string!Topology is such a fascinating branch of mathematics. I think it's because it makes use of principles of mathematics that our monkey brains aren't evolved to intuitively grasp like we can with normal mechanics.
This is a breakdown of the mathematics used to resolve one topological puzzle. Trying to apply it to the above, it looks like they introduce threading and looping which is anti-wise to the original setup, and that allows the puzzle to become mathematically "trivial."
Amazing Rope Trick
Here’s an amazing trick that Curtis McMullen performed in yesterday’s workshop on Quantum Mechanics and Topology, organized by Ryan Grady. McMullen modestly declined to be photographed, so here Grady demonstrates the trick. Step 1: Thread …scilogs.spektrum.de
Although 2 additional loops are placed around the post, the original loop of the cord around the post (and through the ring) is never detached from the post.Well he is removing the rope momentarily to loop it around the post. I think that sequence flips the ring to the outside of the rope where it can be removed.
Yeah, a Moebius strip was the only concept I could rally in trying to comprehend this puzzle.This reminds me of unintuitive geometry, such as the fact that the Moebius strip has only one surface. Cutting a Moebius strip also provides unintuitive results:
OK, I watched the video and now the conceptual gears in my brain are overheating. Of course now I want to know what happens if the original Moebius strip is cut into 3 strips. Predictions anyone?This reminds me of unintuitive geometry, such as the fact that the Moebius strip has only one surface. Cutting a Moebius strip also provides unintuitive results:
Yes, it is like a sailor's knot in which the metal ring is attached to the stick on the outside thanks to the knot.Well he is removing the rope momentarily to loop it around the post. I think that sequence flips the ring to the outside of the rope where it can be removed.
I'm generally pretty adept at grasping and applying concepts, but my mind's apparently missing the file for grasping how these ring/knot tricks could possibly work. Speaking of knots, I read of a research study related to the seeming phenomenon of cords tying themselves in knots. They place 2 strings in a tumbling device, then after each rotation, checked to see if the strings had knotted together. They repeated this process with progressively longer pairs of strings. Inevitably, at some point, the 2 strings tied themselves together!Me thinks knots are magic!
Maybe this picture helps:I'm generally pretty adept at grasping and applying concepts, but my mind's apparently missing the file for grasping how these ring/knot tricks could possibly work.